Superposition of two identical
transparent layers comprising randomly located opaque dots produces moiré
images. This phenomenon is called random moiré. Moiré superposition images are
formed when the patterns of the layers are perfectly matched and one of the
layers is slightly rotated. The figure below animates the superposition optical
image of two layers with identical patterns of random dots. In this animation,
one of the layers rotates, oscillating between 0 and 4 degrees:

Superposition of a transparent
base layer where all opaque dots are replaced by a micro-shape (e.g. a given
letter) with a revealing layer, which is completely opaque except tinny transparent
holes, placed according the same random pattern as the pattern of the shapes in
the base layer, forms a moiré image where the micro shape of the base layer
appears magnified and rotated by +90 degree or by –90 degree.

The figure below animates
superposition of a base layer comprising randomly scattered copies of the
symbol “2” with an opaque revealing layer comprising similarly placed tinny
holes. In this animation, the revealing layer oscillates between –2 degree and
+2 degree. The diameter of holes of this sample is about 4 to 5 times smaller
than the size of the shapes of the base layer.